Relative equilibria and stability of a gyrostat-satellite when the vector of the gyrostatic moment is parallel to the principal central axis of inertia of the satellite

Dynamics of a gyrostat-satellite moving in a central Newtonian force field in a circular orbit is investigated. In specific case, when the vector of the gyrostatic moment is parallel to one of the principal central axes of inertia of the satellite, all equilibrium orientations are determined. For each equilibrium orientation sufficient conditions of stability are obtained as a result of generalized energy integral analysis. Necessary conditions of stability are derived from analysis of linearized equations of motion. Evolution of domains where stability conditions take place is investigated in detail depending on parameters of a problem. All bifurcational values of parameters corresponding to qualitative change of stability domains are found .